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SSM-Tp’s, l=0

SSM-Thom polynomials of contact singularities of relative dimension 0

(Hierarchy of these singularities)

codimension 0

Local algebra C
Thom-Boardman class \Sigma^0
Codimension 0
SSM-Thom polynomial in Chern classes 1-c_{1} T+ c_{1}^2 T^2-c_{1}^3 T^3+ (c_{1}^4-c_{2}^2+ c_{1} c_{3}) T^4+ (-3 c_{1}^2 c_{3}-c_{1}^5+ 3 c_{1} c_{2}^2) T^5+ (3 c_{3}^2+ c_{1}^6+ c_{1} c_{5}-6 c_{1}^2 c_{2}^2+ 2 c_{2}^3-4 c_{2} c_{4}-3 c_{1} c_{2} c_{3}+ 6 c_{1}^3 c_{3}+ c_{1}^2 c_{4}) T^6+ (10 c_{1}^3 c_{2}^2+ 12 c_{1}^2 c_{2} c_{3}-8 c_{1} c_{2}^3-10 c_{1}^4 c_{3}-4 c_{1}^3 c_{4}-4 c_{1}^2 c_{5}-c_{1}^7+ 16 c_{1} c_{2} c_{4}-12 c_{1} c_{3}^2) T^7+ (c_{1} c_{7}+ 16 c_{2}^2 c_{4}-30 c_{1}^3 c_{2} c_{3}+ 6 c_{1} c_{2}^2 c_{3}+ 2 c_{1}^2 c_{6}-6 c_{2} c_{6}-10 c_{1} c_{2} c_{5}+ 11 c_{1}^3 c_{5}-44 c_{1}^2 c_{2} c_{4}+ 4 c_{1} c_{3} c_{4}-3 c_{2}^4-10 c_{4}^2+ 15 c_{3} c_{5}+ c_{1}^8-15 c_{1}^4 c_{2}^2+ 20 c_{1}^2 c_{2}^3+ 15 c_{1}^5 c_{3}+ 30 c_{1}^2 c_{3}^2-12 c_{2} c_{3}^2+ 10 c_{1}^4 c_{4}) T^8
SSM-Thom polynomial in Schur functions s_{0}-s_{1} T+ (s_{1, 1}+ s_{2}) T^2+ (-s_{1, 1, 1}-2 s_{2, 1}-s_{3}) T^3+ (s_{1, 1, 1, 1}+ 3 s_{2, 1, 1}+ s_{2, 2}+ 3 s_{3, 1}+ s_{4}) T^4+ (-s_{1, 1, 1, 1, 1}-4 s_{2, 1, 1, 1}-2 s_{2, 2, 1}-6 s_{3, 1, 1}-2 s_{3, 2}-4 s_{4, 1}-s_{5}) T^5+ (s_{1, 1, 1, 1, 1, 1}+ 5 s_{2, 1, 1, 1, 1}+ 3 s_{2, 2, 1, 1}+ s_{2, 2, 2}+ 10 s_{3, 1, 1, 1}+ 5 s_{3, 2, 1}+ s_{3, 3}+ 10 s_{4, 1, 1}+ 3 s_{4, 2}+ 5 s_{5, 1}+ s_{6}) T^6+ (-s_{1, 1, 1, 1, 1, 1, 1}-6 s_{2, 1, 1, 1, 1, 1}-4 s_{2, 2, 1, 1, 1}-2 s_{2, 2, 2, 1}-15 s_{3, 1, 1, 1, 1}-9 s_{3, 2, 1, 1}-3 s_{3, 2, 2}-3 s_{3, 3, 1}-20 s_{4, 1, 1, 1}-9 s_{4, 2, 1}-2 s_{4, 3}-15 s_{5, 1, 1}-4 s_{5, 2}-6 s_{6, 1}-s_{7}) T^7+ (s_{1, 1, 1, 1, 1, 1, 1, 1}+ 7 s_{2, 1, 1, 1, 1, 1, 1}+ 5 s_{2, 2, 1, 1, 1, 1}+ 3 s_{2, 2, 2, 1, 1}+ s_{2, 2, 2, 2}+ 21 s_{3, 1, 1, 1, 1, 1}+ 14 s_{3, 2, 1, 1, 1}+ 7 s_{3, 2, 2, 1}+ 6 s_{3, 3, 1, 1}+ 3 s_{3, 3, 2}+ 35 s_{4, 1, 1, 1, 1}+ 19 s_{4, 2, 1, 1}+ 6 s_{4, 2, 2}+ 7 s_{4, 3, 1}+ s_{4, 4}+ 35 s_{5, 1, 1, 1}+ 14 s_{5, 2, 1}+ 3 s_{5, 3}+ 21 s_{6, 1, 1}+ 5 s_{6, 2}+ 7 s_{7, 1}+ s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions S_{}

codimension 1

Local algebra C[x]/(x^2)
Thom-Boardman class \Sigma^{1,0}
Codimension 1
SSM-Thom polynomial in Chern classes c_{1} T+ (-2 c_{1}^2-c_{2}) T^2+ (3 c_{1}^3+ c_{3}+ 3 c_{1} c_{2}) T^3+ (-4 c_{1}^4-6 c_{1}^2 c_{2}-7 c_{1} c_{3}+ 3 c_{2}^2-c_{4}) T^4+ (23 c_{1}^2 c_{3}-4 c_{2} c_{3}-13 c_{1} c_{2}^2+ 10 c_{1}^3 c_{2}+ 9 c_{1} c_{4}+ c_{5}+ 5 c_{1}^5) T^5+ (-2 c_{2}^3-17 c_{1} c_{5}-c_{6}-6 c_{1}^6+ 24 c_{2} c_{4}-54 c_{1}^3 c_{3}-15 c_{1}^4 c_{2}+ 25 c_{1} c_{2} c_{3}+ 34 c_{1}^2 c_{2}^2-13 c_{3}^2-38 c_{1}^2 c_{4}) T^6+ (27 c_{1} c_{6}+ 14 c_{1} c_{2}^3+ 7 c_{1}^7-38 c_{2} c_{5}+ c_{7}+ 89 c_{1}^2 c_{5}+ 18 c_{3} c_{4}+ 21 c_{1}^5 c_{2}-144 c_{1} c_{2} c_{4}+ 74 c_{1} c_{3}^2+ 105 c_{1}^4 c_{3}+ 2 c_{2}^2 c_{3}+ 111 c_{1}^3 c_{4}-70 c_{1}^3 c_{2}^2-90 c_{1}^2 c_{2} c_{3}) T^7+ (-8 c_{1}^8-6 c_{2}^4+ 59 c_{4}^2-c_{8}-181 c_{1}^5 c_{3}-244 c_{1}^2 c_{3}^2+ 34 c_{2} c_{3}^2-260 c_{1}^4 c_{4}-54 c_{2}^2 c_{4}-51 c_{1} c_{7}-28 c_{1}^6 c_{2}+ 125 c_{1}^4 c_{2}^2-50 c_{1}^2 c_{2}^3+ 240 c_{1}^3 c_{2} c_{3}-14 c_{1} c_{2}^2 c_{3}+ 509 c_{1}^2 c_{2} c_{4}-135 c_{1} c_{3} c_{4}+ 305 c_{1} c_{2} c_{5}-301 c_{1}^3 c_{5}-122 c_{3} c_{5}-178 c_{1}^2 c_{6}+ 106 c_{2} c_{6}) T^8
SSM-Thom polynomial in Schur functions s_{1} T+ (-2 s_{1, 1}-3 s_{2}) T^2+ (3 s_{1, 1, 1}+ 9 s_{2, 1}+ 7 s_{3}) T^3+ (-4 s_{1, 1, 1, 1}-18 s_{2, 1, 1}-11 s_{2, 2}-28 s_{3, 1}-15 s_{4}) T^4+ (5 s_{1, 1, 1, 1, 1}+ 30 s_{2, 1, 1, 1}+ 32 s_{2, 2, 1}+ 70 s_{3, 1, 1}+ 48 s_{3, 2}+ 75 s_{4, 1}+ 31 s_{5}) T^5+ (-6 s_{1, 1, 1, 1, 1, 1}-45 s_{2, 1, 1, 1, 1}-65 s_{2, 2, 1, 1}-28 s_{2, 2, 2}-140 s_{3, 1, 1, 1}-167 s_{3, 2, 1}-51 s_{3, 3}-225 s_{4, 1, 1}-153 s_{4, 2}-186 s_{5, 1}-63 s_{6}) T^6+ (7 s_{1, 1, 1, 1, 1, 1, 1}+ 63 s_{2, 1, 1, 1, 1, 1}+ 112 s_{2, 2, 1, 1, 1}+ 77 s_{2, 2, 2, 1}+ 245 s_{3, 1, 1, 1, 1}+ 393 s_{3, 2, 1, 1}+ 171 s_{3, 2, 2}+ 211 s_{3, 3, 1}+ 525 s_{4, 1, 1, 1}+ 615 s_{4, 2, 1}+ 210 s_{4, 3}+ 651 s_{5, 1, 1}+ 426 s_{5, 2}+ 441 s_{6, 1}+ 127 s_{7}) T^7+ (-8 s_{1, 1, 1, 1, 1, 1, 1, 1}-84 s_{2, 1, 1, 1, 1, 1, 1}-175 s_{2, 2, 1, 1, 1, 1}-151 s_{2, 2, 2, 1, 1}-58 s_{2, 2, 2, 2}-392 s_{3, 1, 1, 1, 1, 1}-768 s_{3, 2, 1, 1, 1}-532 s_{3, 2, 2, 1}-562 s_{3, 3, 1, 1}-290 s_{3, 3, 2}-1050 s_{4, 1, 1, 1, 1}-1641 s_{4, 2, 1, 1}-701 s_{4, 2, 2}-981 s_{4, 3, 1}-199 s_{4, 4}-1736 s_{5, 1, 1, 1}-1936 s_{5, 2, 1}-641 s_{5, 3}-1764 s_{6, 1, 1}-1099 s_{6, 2}-1016 s_{7, 1}-255 s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions S_{1} T – S_{2} T^2 +( S_{3}+2 S_{2,1} ) T^3 + (-S_{4}-4 S_3,1} ) T^4 + (4 S_{3,1,1} + S_{5} + 6 S_{4,1} ) T^5 + (-12 S_{4,1,1} – S_{6} – 8 S_{5,1} ) T^6 + (24 S_{5,1,1} + 8 S_{4,1,1,1} + S{7} + 10 S_{6,1} ) T^7 +( 40S_{6,1,1} -32 S_{5,1,1,1} – S_{8} – 12 S_{7,1} ) T^8

codimension 2

Local algebra C[x]/(x^3)
Thom-Boardman class \Sigma^{1,1,0}
Codimension 2
SSM-Thom polynomial in Chern classes (c_{2}+ c_{1}^2) T^2+ (-3 c_{1}^3-3 c_{3}-6 c_{1} c_{2}) T^3+ (6 c_{1}^4+ 18 c_{1}^2 c_{2}+ 20 c_{1} c_{3}-c_{2}^2+ 7 c_{4}) T^4+ (-76 c_{1}^2 c_{3}+ 6 c_{2} c_{3}+ 11 c_{1} c_{2}^2-40 c_{1}^3 c_{2}-56 c_{1} c_{4}-15 c_{5}-10 c_{1}^5) T^5+ (-11 c_{2}^3+ 152 c_{1} c_{5}+ 31 c_{6}+ 15 c_{1}^6-53 c_{2} c_{4}+ 211 c_{1}^3 c_{3}+ 75 c_{1}^4 c_{2}-39 c_{1} c_{2} c_{3}-46 c_{1}^2 c_{2}^2+ 22 c_{3}^2+ 245 c_{1}^2 c_{4}) T^6+ (-400 c_{1} c_{6}+ 54 c_{1} c_{2}^3-21 c_{1}^7+ 199 c_{2} c_{5}-63 c_{7}-795 c_{1}^2 c_{5}-79 c_{3} c_{4}-126 c_{1}^5 c_{2}+ 423 c_{1} c_{2} c_{4}-199 c_{1} c_{3}^2-480 c_{1}^4 c_{3}+ 39 c_{2}^2 c_{3}-776 c_{1}^3 c_{4}+ 130 c_{1}^3 c_{2}^2+ 162 c_{1}^2 c_{2} c_{3}) T^7+ (28 c_{1}^8+ 39 c_{2}^4-119 c_{4}^2+ 127 c_{8}+ 953 c_{1}^5 c_{3}+ 907 c_{1}^2 c_{3}^2-17 c_{2} c_{3}^2+ 1997 c_{1}^4 c_{4}-93 c_{2}^2 c_{4}+ 1052 c_{1} c_{7}+ 196 c_{1}^6 c_{2}-295 c_{1}^4 c_{2}^2-155 c_{1}^2 c_{2}^3-512 c_{1}^3 c_{2} c_{3}-290 c_{1} c_{2}^2 c_{3}-1855 c_{1}^2 c_{2} c_{4}+ 769 c_{1} c_{3} c_{4}-1755 c_{1} c_{2} c_{5}+ 2907 c_{1}^3 c_{5}+ 440 c_{3} c_{5}+ 2468 c_{1}^2 c_{6}-742 c_{2} c_{6}) T^8
SSM-Thom polynomial in Schur-tilde functions T^2 (+2 S_{2}+1 S_{1, 1})+T^3 (-6 S_{3}-6 S_{2, 1})+T^4 (+14 S_{4}+26 S_{3, 1}+5 S_{2, 2}+5 S_{2, 1, 1})+T^5 (-30 S_{5}-82 S_{4, 1}-34 S_{3, 2}-38 S_{3, 1, 1}-12 S_{2, 2, 1})+T^6 (+62 S_{6}+222 S_{5, 1}+132 S_{4, 2}+19 S_{3, 3}+180 S_{4, 1, 1}+102 S_{3, 2, 1}+2 S_{2, 2, 2}+19 S_{3, 1, 1, 1}+5 S_{2, 2, 1, 1})+T^7 (-126 S_{7}-554 S_{6, 1}-428 S_{5, 2}-100 S_{4, 3}-656 S_{5, 1, 1}-500 S_{4, 2, 1}-76 S_{3, 3, 1}-20 S_{3, 2, 2}-176 S_{4, 1, 1, 1}-84 S_{3, 2, 1, 1})+T^8 (+254 S_{8}+1318 S_{7, 1}+1228 S_{6, 2}+328 S_{5, 3}+33 S_{4, 4}+2060 S_{6, 1, 1}+1928 S_{5, 2, 1}+489 S_{4, 3, 1}+116 S_{4, 2, 2}+18 S_{3, 3, 2}+968 S_{5, 1, 1, 1}+641 S_{4, 2, 1, 1}+115 S_{3, 3, 1, 1}+12 S_{3, 2, 2, 1}+65 S_{4, 1, 1, 1, 1}+24 S_{3, 2, 1, 1, 1})

codimension 3

Local algebra C[x]/(x^4)
Thom-Boardman class \Sigma^{1,1,1,0}
Codimension 3
SSM-Thom polynomial in Chern classes (2 c_{3}+ 3 c_{1} c_{2}+ c_{1}^3) T^3+ (-4 c_{1}^4-18 c_{1}^2 c_{2}-22 c_{1} c_{3}-4 c_{2}^2-12 c_{4}) T^4+ (116 c_{1}^2 c_{3}+ 14 c_{2} c_{3}+ 19 c_{1} c_{2}^2+ 10 c_{1}^5+ 121 c_{1} c_{4}+ 60 c_{1}^3 c_{2}+ 50 c_{5}) T^5+ (21 c_{2}^3-544 c_{1} c_{5}-180 c_{6}-150 c_{1}^4 c_{2}-94 c_{1} c_{2} c_{3}+ 3 c_{2} c_{4}-29 c_{3}^2-20 c_{1}^6-414 c_{1}^3 c_{3}-647 c_{1}^2 c_{4}-46 c_{1}^2 c_{2}^2) T^6+ (2219 c_{1} c_{6}-168 c_{1} c_{2}^3+ 382 c_{1} c_{3}^2+ 35 c_{1}^7+ 602 c_{7}-181 c_{1} c_{2} c_{4}+ 3187 c_{1}^2 c_{5}+ 2438 c_{1}^3 c_{4}+ 195 c_{3} c_{4}+ 70 c_{1}^3 c_{2}^2+ 355 c_{1}^2 c_{2} c_{3}+ 315 c_{1}^5 c_{2}-251 c_{2} c_{5}+ 1155 c_{1}^4 c_{3}-147 c_{2}^2 c_{3}) T^7+ (-6 c_{4}^2-17 c_{2}^4-2722 c_{1}^5 c_{3}-1932 c_{8}-56 c_{1}^8-7302 c_{1}^4 c_{4}+ 781 c_{2}^2 c_{4}-2315 c_{1}^2 c_{3}^2+ 21 c_{2} c_{3}^2-14496 c_{1}^2 c_{6}+ 1858 c_{2} c_{6}-8554 c_{1} c_{7}-588 c_{1}^6 c_{2}-50 c_{1}^4 c_{2}^2+ 710 c_{1}^2 c_{2}^3-968 c_{1}^3 c_{2} c_{3}+ 1293 c_{1} c_{2}^2 c_{3}+ 1454 c_{1}^2 c_{2} c_{4}-2523 c_{1} c_{3} c_{4}+ 2987 c_{1} c_{2} c_{5}-13183 c_{1}^3 c_{5}-1012 c_{3} c_{5}) T^8
SSM-Thom polynomial in Schur functions (s_{1, 1, 1}+ 5 s_{2, 1}+ 6 s_{3}) T^3+ (-4 s_{1, 1, 1, 1}-30 s_{2, 1, 1}-30 s_{2, 2}-74 s_{3, 1}-60 s_{4}) T^4+ (10 s_{1, 1, 1, 1, 1}+ 100 s_{2, 1, 1, 1}+ 189 s_{2, 2, 1}+ 375 s_{3, 1, 1}+ 398 s_{3, 2}+ 625 s_{4, 1}+ 390 s_{5}) T^5+ (-20 s_{1, 1, 1, 1, 1, 1}-250 s_{2, 1, 1, 1, 1}-676 s_{2, 2, 1, 1}-425 s_{2, 2, 2}-1260 s_{3, 1, 1, 1}-2584 s_{3, 2, 1}-1158 s_{3, 3}-3200 s_{4, 1, 1}-3304 s_{4, 2}-4090 s_{5, 1}-2100 s_{6}) T^6+ (35 s_{1, 1, 1, 1, 1, 1, 1}+ 525 s_{2, 1, 1, 1, 1, 1}+ 1820 s_{2, 2, 1, 1, 1}+ 2037 s_{2, 2, 2, 1}+ 3325 s_{3, 1, 1, 1, 1}+ 9854 s_{3, 2, 1, 1}+ 6249 s_{3, 2, 2}+ 8526 s_{3, 3, 1}+ 11375 s_{4, 1, 1, 1}+ 22730 s_{4, 2, 1}+ 11680 s_{4, 3}+ 22141 s_{5, 1, 1}+ 22046 s_{5, 2}+ 23205 s_{6, 1}+ 10206 s_{7}) T^7+ (-56 s_{1, 1, 1, 1, 1, 1, 1, 1}-980 s_{2, 1, 1, 1, 1, 1, 1}-4110 s_{2, 2, 1, 1, 1, 1}-6300 s_{2, 2, 2, 1, 1}-3131 s_{2, 2, 2, 2}-7476 s_{3, 1, 1, 1, 1, 1}-28532 s_{3, 2, 1, 1, 1}-32254 s_{3, 2, 2, 1}-35766 s_{3, 3, 1, 1}-27263 s_{3, 3, 2}-32200 s_{4, 1, 1, 1, 1}-93030 s_{4, 2, 1, 1}-58132 s_{4, 2, 2}-92514 s_{4, 3, 1}-26998 s_{4, 4}-84448 s_{5, 1, 1, 1}-161988 s_{5, 2, 1}-83374 s_{5, 3}-134610 s_{6, 1, 1}-129570 s_{6, 2}-120498 s_{7, 1}-46620 s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions T^3 (+6 S_{3}+5 S_{2, 1}+1 S_{1, 1, 1})+T^4 (-36 S_{4}-47 S_{3, 1}-15 S_{2, 2}-13 S_{2, 1, 1})+T^5 (+150 S_{5}+281 S_{4, 1}+150 S_{3, 2}+124 S_{3, 1, 1}+53 S_{2, 2, 1}+9 S_{2, 1, 1, 1})+T^6 (-540 S_{6}-1319 S_{5, 1}-924 S_{4, 2}-201 S_{3, 3}-860 S_{4, 1, 1}-638 S_{3, 2, 1}-36 S_{2, 2, 2}-137 S_{3, 1, 1, 1}-59 S_{2, 2, 1, 1})+T^7 (+1806 S_{7}+5405 S_{6, 1}+4632 S_{5, 2}+1740 S_{4, 3}+4794 S_{5, 1, 1}+4600 S_{4, 2, 1}+1115 S_{3, 3, 1}+527 S_{3, 2, 2}+1296 S_{4, 1, 1, 1}+958 S_{3, 2, 1, 1}+91 S_{2, 2, 2, 1}+55 S_{3, 1, 1, 1, 1}+21 S_{2, 2, 1, 1, 1})+T^8 (-5796 S_{8}-20411 S_{7, 1}-20580 S_{6, 2}-9464 S_{5, 3}-1715 S_{4, 4}-23068 S_{6, 1, 1}-26404 S_{5, 2, 1}-10857 S_{4, 3, 1}-4432 S_{4, 2, 2}-1688 S_{3, 3, 2}-9232 S_{5, 1, 1, 1}-8889 S_{4, 2, 1, 1}-2349 S_{3, 3, 1, 1}-1569 S_{3, 2, 2, 1}-23 S_{2, 2, 2, 2}-965 S_{4, 1, 1, 1, 1}-636 S_{3, 2, 1, 1, 1}-59 S_{2, 2, 2, 1, 1})

codimension 4

Local algebra C[x]/(x^5)
Thom-Boardman class \Sigma^{1,1,1,1,0}
Codimension 4
SSM-Thom polynomial in Chern classes (6 c_{4}+ 9 c_{1} c_{3}+ 2 c_{2}^2+ 6 c_{1}^2 c_{2}+ c_{1}^4) T^4+ (-60 c_{5}-87 c_{1}^2 c_{3}-112 c_{1} c_{4}-5 c_{1}^5-40 c_{1}^3 c_{2}-28 c_{2} c_{3}-28 c_{1} c_{2}^2) T^5+ (15 c_{1}^6-c_{2}^3+ 289 c_{1} c_{2} c_{3}+ 446 c_{1}^3 c_{3}+ 144 c_{1}^2 c_{2}^2+ 127 c_{2} c_{4}+ 897 c_{1} c_{5}+ 390 c_{6}+ 150 c_{1}^4 c_{2}+ 852 c_{1}^2 c_{4}+ 51 c_{3}^2) T^6+ (-6587 c_{1}^2 c_{5}+ 92 c_{1} c_{2}^3+ 111 c_{2}^2 c_{3}-678 c_{1} c_{3}^2-480 c_{1}^3 c_{2}^2-2100 c_{7}-1211 c_{1} c_{2} c_{4}-4138 c_{1}^3 c_{4}-35 c_{1}^7-1554 c_{1}^2 c_{2} c_{3}-5768 c_{1} c_{6}-420 c_{1}^5 c_{2}-441 c_{3} c_{4}-371 c_{2} c_{5}-1620 c_{1}^4 c_{3}) T^7+ (2929 c_{1} c_{2} c_{5}+ 70 c_{1}^8-90 c_{2}^4+ 569 c_{4}^2+ 10206 c_{8}+ 4705 c_{1}^5 c_{3}+ 4743 c_{1}^2 c_{3}^2-53 c_{2} c_{3}^2+ 15151 c_{1}^4 c_{4}-1269 c_{2}^2 c_{4}+ 32726 c_{1}^3 c_{5}+ 2325 c_{3} c_{5}+ 43934 c_{1}^2 c_{6}-164 c_{2} c_{6}+ 32781 c_{1} c_{7}+ 980 c_{1}^6 c_{2}+ 1245 c_{1}^4 c_{2}^2-725 c_{1}^2 c_{2}^3+ 5874 c_{1}^3 c_{2} c_{3}-1555 c_{1} c_{2}^2 c_{3}+ 6057 c_{1}^2 c_{2} c_{4}+ 6385 c_{1} c_{3} c_{4}) T^8
SSM-Thom polynomial in Schur functions (s_{1, 1, 1, 1}+ 9 s_{2, 1, 1}+ 10 s_{2, 2}+ 26 s_{3, 1}+ 24 s_{4}) T^4+ (-5 s_{1, 1, 1, 1, 1}-60 s_{2, 1, 1, 1}-133 s_{2, 2, 1}-265 s_{3, 1, 1}-316 s_{3, 2}-510 s_{4, 1}-360 s_{5}) T^5+ (15 s_{1, 1, 1, 1, 1, 1}+ 225 s_{2, 1, 1, 1, 1}+ 729 s_{2, 2, 1, 1}+ 518 s_{2, 2, 2}+ 1340 s_{3, 1, 1, 1}+ 3195 s_{3, 2, 1}+ 1598 s_{3, 3}+ 3960 s_{4, 1, 1}+ 4554 s_{4, 2}+ 5800 s_{5, 1}+ 3360 s_{6}) T^6+ (-35 s_{1, 1, 1, 1, 1, 1, 1}-630 s_{2, 1, 1, 1, 1, 1}-2650 s_{2, 2, 1, 1, 1}-3458 s_{2, 2, 2, 1}-4725 s_{3, 1, 1, 1, 1}-16635 s_{3, 2, 1, 1}-11742 s_{3, 2, 2}-16494 s_{3, 3, 1}-18900 s_{4, 1, 1, 1}-43472 s_{4, 2, 1}-24848 s_{4, 3}-42490 s_{5, 1, 1}-46784 s_{5, 2}-50820 s_{6, 1}-25200 s_{7}) T^7+ (70 s_{1, 1, 1, 1, 1, 1, 1, 1}+ 1470 s_{2, 1, 1, 1, 1, 1, 1}+ 7545 s_{2, 2, 1, 1, 1, 1}+ 13790 s_{2, 2, 2, 1, 1}+ 7555 s_{2, 2, 2, 2}+ 13300 s_{3, 1, 1, 1, 1, 1}+ 61204 s_{3, 2, 1, 1, 1}+ 79583 s_{3, 2, 2, 1}+ 89575 s_{3, 3, 1, 1}+ 75322 s_{3, 3, 2}+ 67200 s_{4, 1, 1, 1, 1}+ 228712 s_{4, 2, 1, 1}+ 157710 s_{4, 2, 2}+ 259895 s_{4, 3, 1}+ 83758 s_{4, 4}+ 204631 s_{5, 1, 1, 1}+ 448604 s_{5, 2, 1}+ 256462 s_{5, 3}+ 375039 s_{6, 1, 1}+ 397458 s_{6, 2}+ 382326 s_{7, 1}+ 166824 s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions T^4 (+24 S_{4}+26 S_{3, 1}+10 S_{2, 2}+9 S_{2, 1, 1}+1 S_{1, 1, 1, 1})+T^5 (-240 S_{5}-358 S_{4, 1}-208 S_{3, 2}-160 S_{3, 1, 1}-76 S_{2, 2, 1}-22 S_{2, 1, 1, 1})+T^6 (+1560 S_{6}+3006 S_{5, 1}+2202 S_{4, 2}+596 S_{3, 3}+1782 S_{4, 1, 1}+1413 S_{3, 2, 1}+129 S_{2, 2, 2}+358 S_{3, 1, 1, 1}+180 S_{2, 2, 1, 1}+14 S_{2, 1, 1, 1, 1})+T^7 (-8400 S_{7}-19790 S_{6, 1}-17194 S_{5, 2}-7590 S_{4, 3}-15082 S_{5, 1, 1}-15314 S_{4, 2, 1}-4522 S_{3, 3, 1}-2512 S_{3, 2, 2}-4260 S_{4, 1, 1, 1}-3622 S_{3, 2, 1, 1}-500 S_{2, 2, 2, 1}-348 S_{3, 1, 1, 1, 1}-170 S_{2, 2, 1, 1, 1})+T^8 (+40824 S_{8}+113086 S_{7, 1}+113158 S_{6, 2}+60924 S_{5, 3}+13788 S_{4, 4}+106534 S_{6, 1, 1}+127522 S_{5, 2, 1}+61803 S_{4, 3, 1}+28488 S_{4, 2, 2}+12183 S_{3, 3, 2}+40228 S_{5, 1, 1, 1}+43803 S_{4, 2, 1, 1}+13653 S_{3, 3, 1, 1}+10798 S_{3, 2, 2, 1}+310 S_{2, 2, 2, 2}+5383 S_{4, 1, 1, 1, 1}+4442 S_{3, 2, 1, 1, 1}+655 S_{2, 2, 2, 1, 1}+125 S_{3, 1, 1, 1, 1, 1}+56 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(x^2,y^2)
Thom-Boardman class \Sigma^{2,0}
Codimension 4
SSM-Thom polynomial in Chern classes (-c_{1} c_{3}+ c_{2}^2) T^4+ (-2 c_{2} c_{3}-4 c_{1} c_{2}^2+ 2 c_{1} c_{4}+ 4 c_{1}^2 c_{3}) T^5+ (-2 c_{3}^2-c_{2}^3+ 7 c_{2} c_{4}-11 c_{1}^2 c_{4}+ 12 c_{1} c_{2} c_{3}-10 c_{1}^3 c_{3}-5 c_{1} c_{5}+ 10 c_{1}^2 c_{2}^2) T^6+ (-20 c_{1}^3 c_{2}^2+ 35 c_{1}^3 c_{4}+ 31 c_{1}^2 c_{5}+ 7 c_{1} c_{2}^3+ 20 c_{1}^4 c_{3}+ 10 c_{1} c_{3}^2+ 3 c_{2}^2 c_{3}-44 c_{1} c_{2} c_{4}-42 c_{1}^2 c_{2} c_{3}+ 10 c_{1} c_{6}+ 3 c_{3} c_{4}-13 c_{2} c_{5}) T^7+ (-112 c_{1}^3 c_{5}-31 c_{3} c_{5}+ 110 c_{1}^3 c_{2} c_{3}-21 c_{1} c_{2}^2 c_{3}-85 c_{1}^4 c_{4}-22 c_{2}^2 c_{4}+ 109 c_{1} c_{2} c_{5}-3 c_{2}^4+ 164 c_{1}^2 c_{2} c_{4}-21 c_{1} c_{3} c_{4}+ 36 c_{2} c_{6}-21 c_{1} c_{7}+ 16 c_{4}^2-74 c_{1}^2 c_{6}+ 35 c_{1}^4 c_{2}^2-25 c_{1}^2 c_{2}^3-35 c_{1}^5 c_{3}-28 c_{1}^2 c_{3}^2+ 8 c_{2} c_{3}^2) T^8
SSM-Thom polynomial in Schur functions s_{2, 2} T^4+ (-4 s_{2, 2, 1}-6 s_{3, 2}) T^5+ (10 s_{2, 2, 1, 1}+ 9 s_{2, 2, 2}+ 30 s_{3, 2, 1}+ 19 s_{3, 3}+ 25 s_{4, 2}) T^6+ (-20 s_{2, 2, 1, 1, 1}-33 s_{2, 2, 2, 1}-88 s_{3, 2, 1, 1}-78 s_{3, 2, 2}-110 s_{3, 3, 1}-144 s_{4, 2, 1}-118 s_{4, 3}-86 s_{5, 2}) T^7+ (35 s_{2, 2, 1, 1, 1, 1}+ 80 s_{2, 2, 2, 1, 1}+ 42 s_{2, 2, 2, 2}+ 200 s_{3, 2, 1, 1, 1}+ 320 s_{3, 2, 2, 1}+ 360 s_{3, 3, 1, 1}+ 319 s_{3, 3, 2}+ 475 s_{4, 2, 1, 1}+ 406 s_{4, 2, 2}+ 753 s_{4, 3, 1}+ 253 s_{4, 4}+ 550 s_{5, 2, 1}+ 487 s_{5, 3}+ 261 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^4 (+1 S_{2, 2})+T^5 (-3 S_{3, 2}-1 S_{2, 2, 1})+T^6 (+7 S_{4, 2}+3 S_{3, 3}+8 S_{3, 2, 1}+1 S_{2, 2, 2})+T^7 (-11 S_{5, 2}-15 S_{4, 3}-24 S_{4, 2, 1}-12 S_{3, 3, 1}-4 S_{3, 2, 2}-3 S_{3, 2, 1, 1})+T^8 (+15 S_{6, 2}+31 S_{5, 3}+13 S_{4, 4}+50 S_{5, 2, 1}+64 S_{4, 3, 1}+10 S_{4, 2, 2}+10 S_{3, 3, 2}+24 S_{4, 2, 1, 1}+12 S_{3, 3, 1, 1}+3 S_{3, 2, 2, 1})

codimension 5

Local algebra C[x]/(x^6)
Thom-Boardman class \Sigma^{1,1,1,1,1,0}
Codimension 5
SSM-Thom polynomial in Chern classes (c_{1}^5+ 10 c_{1}^3 c_{2}+ 25 c_{1}^2 c_{3}+ 10 c_{1} c_{2}^2+ 38 c_{1} c_{4}+ 12 c_{2} c_{3}+ 24 c_{5}) T^5+ (-6 c_{1}^6-75 c_{1}^4 c_{2}-247 c_{1}^3 c_{3}-113 c_{1}^2 c_{2}^2-553 c_{1}^2 c_{4}-260 c_{1} c_{2} c_{3}-12 c_{2}^3-690 c_{1} c_{5}-156 c_{2} c_{4}-48 c_{3}^2-360 c_{6}) T^6+ (21 c_{1}^7+ 315 c_{1}^5 c_{2}+ 1317 c_{1}^4 c_{3}+ 608 c_{1}^3 c_{2}^2+ 3919 c_{1}^3 c_{4}+ 2113 c_{1}^2 c_{2} c_{3}+ 93 c_{1} c_{2}^3+ 7322 c_{1}^2 c_{5}+ 2407 c_{1} c_{2} c_{4}+ 817 c_{1} c_{3}^2+ 108 c_{2}^2 c_{3}+ 7624 c_{1} c_{6}+ 1224 c_{2} c_{5}+ 672 c_{3} c_{4}+ 3360 c_{7}) T^7+ (-56 c_{1}^8-980 c_{1}^6 c_{2}-5032 c_{1}^5 c_{3}-2248 c_{1}^4 c_{2}^2-18788 c_{1}^4 c_{4}-10748 c_{1}^3 c_{2} c_{3}-214 c_{1}^2 c_{2}^3-47184 c_{1}^3 c_{5}-17558 c_{1}^2 c_{2} c_{4}-6880 c_{1}^2 c_{3}^2-522 c_{1} c_{2}^2 c_{3}+ 100 c_{2}^4-74386 c_{1}^2 c_{6}-17106 c_{1} c_{2} c_{5}-11242 c_{1} c_{3} c_{4}+ 236 c_{2}^2 c_{4}-332 c_{2} c_{3}^2-66156 c_{1} c_{7}-7056 c_{2} c_{6}-4632 c_{3} c_{5}-1536 c_{4}^2-25200 c_{8}) T^8
SSM-Thom polynomial in Schur functions (120 s_{5}+ 92 s_{3, 2}+ 154 s_{4, 1}+ 35 s_{2, 2, 1}+ 71 s_{3, 1, 1}+ 14 s_{2, 1, 1, 1}+ s_{1, 1, 1, 1, 1}) T^5+ (-2520 s_{6}-1048 s_{3, 3}-3010 s_{4, 2}-3954 s_{5, 1}-305 s_{2, 2, 2}-1926 s_{3, 2, 1}-2415 s_{4, 1, 1}-392 s_{2, 2, 1, 1}-720 s_{3, 1, 1, 1}-105 s_{2, 1, 1, 1, 1}-6 s_{1, 1, 1, 1, 1, 1}) T^6+ (31920 s_{7}+ 27604 s_{4, 3}+ 52266 s_{5, 2}+ 58604 s_{6, 1}+ 11765 s_{3, 2, 2}+ 16935 s_{3, 3, 1}+ 44547 s_{4, 2, 1}+ 44044 s_{5, 1, 1}+ 3178 s_{2, 2, 2, 1}+ 15358 s_{3, 2, 1, 1}+ 17395 s_{4, 1, 1, 1}+ 2162 s_{2, 2, 1, 1, 1}+ 3815 s_{3, 1, 1, 1, 1}+ 441 s_{2, 1, 1, 1, 1, 1}+ 21 s_{1, 1, 1, 1, 1, 1, 1}) T^7+ (-56 s_{1, 1, 1, 1, 1, 1, 1, 1}-1372 s_{2, 1, 1, 1, 1, 1, 1}-8268 s_{2, 2, 1, 1, 1, 1}-17346 s_{2, 2, 2, 1, 1}-10294 s_{2, 2, 2, 2}-14336 s_{3, 1, 1, 1, 1, 1}-76392 s_{3, 2, 1, 1, 1}-110706 s_{3, 2, 2, 1}-126300 s_{3, 3, 1, 1}-114304 s_{3, 3, 2}-82810 s_{4, 1, 1, 1, 1}-319788 s_{4, 2, 1, 1}-237566 s_{4, 2, 2}-402398 s_{4, 3, 1}-140044 s_{4, 4}-285404 s_{5, 1, 1, 1}-691896 s_{5, 2, 1}-427716 s_{5, 3}-586138 s_{6, 1, 1}-666452 s_{6, 2}-662844 s_{7, 1}-317520 s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions T^5 (+120 S_{5}+154 S_{4, 1}+92 S_{3, 2}+71 S_{3, 1, 1}+35 S_{2, 2, 1}+14 S_{2, 1, 1, 1}+1 S_{1, 1, 1, 1, 1})+T^6 (-1800 S_{6}-2944 S_{5, 1}-2180 S_{4, 2}-680 S_{3, 3}-1669 S_{4, 1, 1}-1332 S_{3, 2, 1}-165 S_{2, 2, 2}-394 S_{3, 1, 1, 1}-210 S_{2, 2, 1, 1}-33 S_{2, 1, 1, 1, 1})+T^7 (+16800 S_{7}+33470 S_{6, 1}+28910 S_{5, 2}+13830 S_{4, 3}+23333 S_{5, 1, 1}+23803 S_{4, 2, 1}+7876 S_{3, 3, 1}+4764 S_{3, 2, 2}+6928 S_{4, 1, 1, 1}+6148 S_{3, 2, 1, 1}+1013 S_{2, 2, 2, 1}+809 S_{3, 1, 1, 1, 1}+437 S_{2, 2, 1, 1, 1}+20 S_{2, 1, 1, 1, 1, 1})+T^8 (-126000 S_{8}-294860 S_{7, 1}-289092 S_{6, 2}-167088 S_{5, 3}-43320 S_{4, 4}-247565 S_{6, 1, 1}-296529 S_{5, 2, 1}-155687 S_{4, 3, 1}-76719 S_{4, 2, 2}-34582 S_{3, 3, 2}-91728 S_{5, 1, 1, 1}-103956 S_{4, 2, 1, 1}-35620 S_{3, 3, 1, 1}-29533 S_{3, 2, 2, 1}-1281 S_{2, 2, 2, 2}-14557 S_{4, 1, 1, 1, 1}-13181 S_{3, 2, 1, 1, 1}-2353 S_{2, 2, 2, 1, 1}-730 S_{3, 1, 1, 1, 1, 1}-382 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^2+y^3)
Thom-Boardman class \Sigma^{2,0}
Codimension 5
SSM-Thom polynomial in Chern classes (-2 c_{1}^2 c_{3}+ 2 c_{1} c_{2}^2-2 c_{1} c_{4}+ 2 c_{2} c_{3}) T^5+ (10 c_{1}^3 c_{3}-10 c_{1}^2 c_{2}^2+ 17 c_{1}^2 c_{4}-14 c_{1} c_{2} c_{3}-3 c_{2}^3+ 10 c_{1} c_{5}-9 c_{2} c_{4}-c_{3}^2) T^6+ (-30 c_{1}^4 c_{3}+ 30 c_{1}^3 c_{2}^2-74 c_{1}^3 c_{4}+ 62 c_{1}^2 c_{2} c_{3}+ 12 c_{1} c_{2}^3-87 c_{1}^2 c_{5}+ 81 c_{1} c_{2} c_{4}-3 c_{1} c_{3}^2+ 9 c_{2}^2 c_{3}-40 c_{1} c_{6}+ 41 c_{2} c_{5}-c_{3} c_{4}) T^7+ (70 c_{1}^5 c_{3}-70 c_{1}^4 c_{2}^2+ 229 c_{1}^4 c_{4}-204 c_{1}^3 c_{2} c_{3}-25 c_{1}^2 c_{2}^3+ 402 c_{1}^3 c_{5}-389 c_{1}^2 c_{2} c_{4}+ 31 c_{1}^2 c_{3}^2-58 c_{1} c_{2}^2 c_{3}+ 14 c_{2}^4+ 368 c_{1}^2 c_{6}-381 c_{1} c_{2} c_{5}+ 33 c_{1} c_{3} c_{4}-17 c_{2}^2 c_{4}-3 c_{2} c_{3}^2+ 140 c_{1} c_{7}-160 c_{2} c_{6}+ 37 c_{3} c_{5}-17 c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (4 s_{3, 2}+ 2 s_{2, 2, 1}) T^5+ (-28 s_{3, 3}-40 s_{4, 2}-13 s_{2, 2, 2}-40 s_{3, 2, 1}-10 s_{2, 2, 1, 1}) T^6+ (312 s_{4, 3}+ 252 s_{5, 2}+ 197 s_{3, 2, 2}+ 256 s_{3, 3, 1}+ 358 s_{4, 2, 1}+ 72 s_{2, 2, 2, 1}+ 176 s_{3, 2, 1, 1}+ 30 s_{2, 2, 1, 1, 1}) T^7+ (-70 s_{2, 2, 1, 1, 1, 1}-235 s_{2, 2, 2, 1, 1}-151 s_{2, 2, 2, 2}-534 s_{3, 2, 1, 1, 1}-1134 s_{3, 2, 2, 1}-1156 s_{3, 3, 1, 1}-1228 s_{3, 3, 2}-1614 s_{4, 2, 1, 1}-1675 s_{4, 2, 2}-2870 s_{4, 3, 1}-1028 s_{4, 4}-2294 s_{5, 2, 1}-2132 s_{5, 3}-1284 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^5 (+4 S_{3, 2}+2 S_{2, 2, 1})+T^6 (-24 S_{4, 2}-12 S_{3, 3}-22 S_{3, 2, 1}-5 S_{2, 2, 2}-2 S_{2, 2, 1, 1})+T^7 (+92 S_{5, 2}+100 S_{4, 3}+134 S_{4, 2, 1}+72 S_{3, 3, 1}+52 S_{3, 2, 2}+32 S_{3, 2, 1, 1}+10 S_{2, 2, 2, 1})+T^8 (-292 S_{6, 2}-460 S_{5, 3}-136 S_{4, 4}-584 S_{5, 2, 1}-644 S_{4, 3, 1}-303 S_{4, 2, 2}-182 S_{3, 3, 2}-252 S_{4, 2, 1, 1}-138 S_{3, 3, 1, 1}-137 S_{3, 2, 2, 1}-2 S_{2, 2, 2, 2}-12 S_{3, 2, 1, 1, 1}-3 S_{2, 2, 2, 1, 1})

codimension 6

Local algebra C[x]/(x^7)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,0}
Codimension 6
SSM-Thom polynomial in Chern classes (c_{1}^6+ 15 c_{1}^4 c_{2}+ 55 c_{1}^3 c_{3}+ 30 c_{1}^2 c_{2}^2+ 141 c_{1}^2 c_{4}+ 79 c_{1} c_{2} c_{3}+ 5 c_{2}^3+ 202 c_{1} c_{5}+ 55 c_{2} c_{4}+ 17 c_{3}^2+ 120 c_{6}) T^6+ (-7 c_{1}^7-126 c_{1}^5 c_{2}-576 c_{1}^4 c_{3}-334 c_{1}^3 c_{2}^2-1952 c_{1}^3 c_{4}-1290 c_{1}^2 c_{2} c_{3}-118 c_{1} c_{2}^3-4175 c_{1}^2 c_{5}-1765 c_{1} c_{2} c_{4}-532 c_{1} c_{3}^2-171 c_{2}^2 c_{3}-4986 c_{1} c_{6}-1089 c_{2} c_{5}-519 c_{3} c_{4}-2520 c_{7}) T^7+ (28 c_{1}^8+ 588 c_{1}^6 c_{2}+ 3263 c_{1}^5 c_{3}+ 1903 c_{1}^4 c_{2}^2+ 13823 c_{1}^4 c_{4}+ 9846 c_{1}^3 c_{2} c_{3}+ 901 c_{1}^2 c_{2}^3+ 39534 c_{1}^3 c_{5}+ 19747 c_{1}^2 c_{2} c_{4}+ 6236 c_{1}^2 c_{3}^2+ 2565 c_{1} c_{2}^2 c_{3}+ 71234 c_{1}^2 c_{6}+ 23891 c_{1} c_{2} c_{5}+ 11945 c_{1} c_{3} c_{4}+ 1315 c_{2}^2 c_{4}+ 857 c_{2} c_{3}^2+ 72692 c_{1} c_{7}+ 12588 c_{2} c_{6}+ 5767 c_{3} c_{5}+ 1997 c_{4}^2+ 31920 c_{8}) T^8
SSM-Thom polynomial in Schur functions (720 s_{6}+ 266 s_{3, 3}+ 770 s_{4, 2}+ 1044 s_{5, 1}+ 70 s_{2, 2, 2}+ 455 s_{3, 2, 1}+ 580 s_{4, 1, 1}+ 84 s_{2, 2, 1, 1}+ 155 s_{3, 1, 1, 1}+ 20 s_{2, 1, 1, 1, 1}+ s_{1, 1, 1, 1, 1, 1}) T^6+ (-20160 s_{7}-15524 s_{4, 3}-29648 s_{5, 2}-34272 s_{6, 1}-6044 s_{3, 2, 2}-8902 s_{3, 3, 1}-23458 s_{4, 2, 1}-23548 s_{5, 1, 1}-1514 s_{2, 2, 2, 1}-7393 s_{3, 2, 1, 1}-8400 s_{4, 1, 1, 1}-936 s_{2, 2, 1, 1, 1}-1645 s_{3, 1, 1, 1, 1}-168 s_{2, 1, 1, 1, 1, 1}-7 s_{1, 1, 1, 1, 1, 1, 1}) T^7+ (28 s_{1, 1, 1, 1, 1, 1, 1, 1}+ 784 s_{2, 1, 1, 1, 1, 1, 1}+ 5403 s_{2, 2, 1, 1, 1, 1}+ 12686 s_{2, 2, 2, 1, 1}+ 8039 s_{2, 2, 2, 2}+ 9282 s_{3, 1, 1, 1, 1, 1}+ 55828 s_{3, 2, 1, 1, 1}+ 88317 s_{3, 2, 2, 1}+ 102114 s_{3, 3, 1, 1}+ 97939 s_{3, 3, 2}+ 60200 s_{4, 1, 1, 1, 1}+ 257655 s_{4, 2, 1, 1}+ 203121 s_{4, 2, 2}+ 352227 s_{4, 3, 1}+ 130582 s_{4, 4}+ 230762 s_{5, 1, 1, 1}+ 606318 s_{5, 2, 1}+ 398938 s_{5, 3}+ 521976 s_{6, 1, 1}+ 627144 s_{6, 2}+ 643608 s_{7, 1}+ 332640 s_{8}) T^8
SSM-Thom polynomial in Schur-tilde functions T^6 (+720 S_{6}+1044 S_{5, 1}+770 S_{4, 2}+266 S_{3, 3}+580 S_{4, 1, 1}+455 S_{3, 2, 1}+70 S_{2, 2, 2}+155 S_{3, 1, 1, 1}+84 S_{2, 2, 1, 1}+20 S_{2, 1, 1, 1, 1}+1 S_{1, 1, 1, 1, 1, 1})+T^7 (-15120 S_{7}-26568 S_{6, 1}-22666 S_{5, 2}-11380 S_{4, 3}-17516 S_{5, 1, 1}-17588 S_{4, 2, 1}-6284 S_{3, 3, 1}-4014 S_{3, 2, 2}-5460 S_{4, 1, 1, 1}-4856 S_{3, 2, 1, 1}-898 S_{2, 2, 2, 1}-810 S_{3, 1, 1, 1, 1}-456 S_{2, 2, 1, 1, 1}-46 S_{2, 1, 1, 1, 1, 1})+T^8 (+191520 S_{8}+394668 S_{7, 1}+378618 S_{6, 2}+227324 S_{5, 3}+64890 S_{4, 4}+306480 S_{6, 1, 1}+361242 S_{5, 2, 1}+198496 S_{4, 3, 1}+102578 S_{4, 2, 2}+47668 S_{3, 3, 2}+113404 S_{5, 1, 1, 1}+129085 S_{4, 2, 1, 1}+47112 S_{3, 3, 1, 1}+39631 S_{3, 2, 2, 1}+2303 S_{2, 2, 2, 2}+20485 S_{4, 1, 1, 1, 1}+19176 S_{3, 2, 1, 1, 1}+3808 S_{2, 2, 2, 1, 1}+1576 S_{3, 1, 1, 1, 1, 1}+887 S_{2, 2, 1, 1, 1, 1}+27 S_{2, 1, 1, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^2+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 6
SSM-Thom polynomial in Chern classes (-2 c_{1}^3 c_{3}+ 2 c_{1}^2 c_{2}^2-5 c_{1}^2 c_{4}+ 2 c_{1} c_{2} c_{3}+ 3 c_{2}^3-6 c_{1} c_{5}+ 9 c_{2} c_{4}-3 c_{3}^2) T^6+ (12 c_{1}^4 c_{3}-12 c_{1}^3 c_{2}^2+ 41 c_{1}^3 c_{4}-14 c_{1}^2 c_{2} c_{3}-27 c_{1} c_{2}^3+ 81 c_{1}^2 c_{5}-86 c_{1} c_{2} c_{4}+ 34 c_{1} c_{3}^2-29 c_{2}^2 c_{3}+ 54 c_{1} c_{6}-67 c_{2} c_{5}+ 13 c_{3} c_{4}) T^7+ (-42 c_{1}^5 c_{3}+ 42 c_{1}^4 c_{2}^2-184 c_{1}^4 c_{4}+ 68 c_{1}^3 c_{2} c_{3}+ 116 c_{1}^2 c_{2}^3-507 c_{1}^3 c_{5}+ 466 c_{1}^2 c_{2} c_{4}-205 c_{1}^2 c_{3}^2+ 249 c_{1} c_{2}^2 c_{3}-3 c_{2}^4-664 c_{1}^2 c_{6}+ 713 c_{1} c_{2} c_{5}-213 c_{1} c_{3} c_{4}+ 123 c_{2}^2 c_{4}+ 41 c_{2} c_{3}^2-336 c_{1} c_{7}+ 400 c_{2} c_{6}-60 c_{3} c_{5}-4 c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (4 s_{3, 3}+ 16 s_{4, 2}+ 5 s_{2, 2, 2}+ 12 s_{3, 2, 1}+ 2 s_{2, 2, 1, 1}) T^6+ (-196 s_{4, 3}-244 s_{5, 2}-160 s_{3, 2, 2}-140 s_{3, 3, 1}-282 s_{4, 2, 1}-51 s_{2, 2, 2, 1}-104 s_{3, 2, 1, 1}-12 s_{2, 2, 1, 1, 1}) T^7+ (42 s_{2, 2, 1, 1, 1, 1}+ 242 s_{2, 2, 2, 1, 1}+ 197 s_{2, 2, 2, 2}+ 468 s_{3, 2, 1, 1, 1}+ 1408 s_{3, 2, 2, 1}+ 1074 s_{3, 3, 1, 1}+ 1477 s_{3, 3, 2}+ 1902 s_{4, 2, 1, 1}+ 2422 s_{4, 2, 2}+ 3232 s_{4, 3, 1}+ 1060 s_{4, 4}+ 3396 s_{5, 2, 1}+ 2800 s_{5, 3}+ 2256 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^6 (+16 S_{4, 2}+4 S_{3, 3}+12 S_{3, 2, 1}+5 S_{2, 2, 2}+2 S_{2, 2, 1, 1})+T^7 (-164 S_{5, 2}-116 S_{4, 3}-186 S_{4, 2, 1}-80 S_{3, 3, 1}-97 S_{3, 2, 2}-50 S_{3, 2, 1, 1}-23 S_{2, 2, 2, 1}-2 S_{2, 2, 1, 1, 1})+T^8 (+1032 S_{6, 2}+1188 S_{5, 3}+308 S_{4, 4}+1598 S_{5, 2, 1}+1356 S_{4, 3, 1}+992 S_{4, 2, 2}+529 S_{3, 3, 2}+646 S_{4, 2, 1, 1}+318 S_{3, 3, 1, 1}+456 S_{3, 2, 2, 1}+29 S_{2, 2, 2, 2}+60 S_{3, 2, 1, 1, 1}+27 S_{2, 2, 2, 1, 1})
Local algebra C[x,y]/(xy,x^3+y^3)
Thom-Boardman class \Sigma^{2,0}
Codimension 6
SSM-Thom polynomial in Chern classes (-c_{1}^3 c_{3}+ c_{1}^2 c_{2}^2-2 c_{1}^2 c_{4}+ 3 c_{1} c_{2} c_{3}-c_{2}^3-3 c_{2} c_{4}+ 3 c_{3}^2) T^6+ (6 c_{1}^4 c_{3}-6 c_{1}^3 c_{2}^2+ 17 c_{1}^3 c_{4}-21 c_{1}^2 c_{2} c_{3}+ 4 c_{1} c_{2}^3+ 10 c_{1}^2 c_{5}+ 17 c_{1} c_{2} c_{4}-30 c_{1} c_{3}^2+ 3 c_{2}^2 c_{3}+ 17 c_{2} c_{5}-17 c_{3} c_{4}) T^7+ (-21 c_{1}^5 c_{3}+ 21 c_{1}^4 c_{2}^2-78 c_{1}^4 c_{4}+ 90 c_{1}^3 c_{2} c_{3}-12 c_{1}^2 c_{2}^3-92 c_{1}^3 c_{5}-37 c_{1}^2 c_{2} c_{4}+ 149 c_{1}^2 c_{3}^2-23 c_{1} c_{2}^2 c_{3}+ 3 c_{2}^4-40 c_{1}^2 c_{6}-124 c_{1} c_{2} c_{5}+ 174 c_{1} c_{3} c_{4}-9 c_{2}^2 c_{4}-c_{2} c_{3}^2-70 c_{2} c_{6}+ 54 c_{3} c_{5}+ 16 c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (6 s_{3, 3}+ 2 s_{4, 2}+ 3 s_{3, 2, 1}+ s_{2, 2, 1, 1}) T^6+ (-96 s_{4, 3}-26 s_{5, 2}-24 s_{3, 2, 2}-75 s_{3, 3, 1}-51 s_{4, 2, 1}-8 s_{2, 2, 2, 1}-31 s_{3, 2, 1, 1}-6 s_{2, 2, 1, 1, 1}) T^7+ (21 s_{2, 2, 1, 1, 1, 1}+ 51 s_{2, 2, 2, 1, 1}+ 33 s_{2, 2, 2, 2}+ 150 s_{3, 2, 1, 1, 1}+ 262 s_{3, 2, 2, 1}+ 468 s_{3, 3, 1, 1}+ 435 s_{3, 3, 2}+ 399 s_{4, 2, 1, 1}+ 363 s_{4, 2, 2}+ 1179 s_{4, 3, 1}+ 590 s_{4, 4}+ 462 s_{5, 2, 1}+ 842 s_{5, 3}+ 192 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^6 (+2 S_{4, 2}+6 S_{3, 3}+3 S_{3, 2, 1}+1 S_{2, 2, 1, 1})+T^7 (-16 S_{5, 2}-64 S_{4, 3}-33 S_{4, 2, 1}-45 S_{3, 3, 1}-12 S_{3, 2, 2}-16 S_{3, 2, 1, 1}-4 S_{2, 2, 2, 1}-1 S_{2, 2, 1, 1, 1})+T^8 (+66 S_{6, 2}+356 S_{5, 3}+210 S_{4, 4}+187 S_{5, 2, 1}+520 S_{4, 3, 1}+124 S_{4, 2, 2}+132 S_{3, 3, 2}+134 S_{4, 2, 1, 1}+133 S_{3, 3, 1, 1}+74 S_{3, 2, 2, 1}+4 S_{2, 2, 2, 2}+21 S_{3, 2, 1, 1, 1}+6 S_{2, 2, 2, 1, 1})

codimension 7

Local algebra C[x]/(x^8)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,1,0}
Codimension 7
SSM-Thom polynomial in Chern classes (-8*c[1]^8-196*c[1]^6*c[2]-1178*c[1]^5*c[3]-810*c[1]^4*c[2]^2-5577*c[1]^4*
c[4]-4588*c[1]^3*c[2]*c[3]-615*c[1]^2*c[2]^3-17886*c[1]^3*c[5]-10567*c[1]^2*c[2
]*c[4]-3101*c[1]^2*c[3]^2-1978*c[1]*c[2]^2*c[3]-40*c[2]^4-36128*c[1]^2*c[6]-\
14706*c[1]*c[2]*c[5]-6758*c[1]*c[3]*c[4]-1280*c[2]^2*c[4]-712*c[2]*c[3]^2-41232
*c[1]*c[7]-8904*c[2]*c[6]-3720*c[3]*c[5]-1296*c[4]^2-20160*c[8])*T^8+(c[1]^7+21
*c[1]^5*c[2]+105*c[1]^4*c[3]+70*c[1]^3*c[2]^2+399*c[1]^3*c[4]+301*c[1]^2*c[2]*c
[3]+35*c[1]*c[2]^3+960*c[1]^2*c[5]+467*c[1]*c[2]*c[4]+139*c[1]*c[3]^2+58*c[2]^2
*c[3]+1284*c[1]*c[6]+326*c[2]*c[5]+154*c[3]*c[4]+720*c[7])*T^7
SSM-Thom polynomial in Schur functions ((T^7*(5040*S[[7]]+3500*S[[4, 3]]+6746*S[[5, 2]]+8028*S[[6, 1]]+1255*S[[3, 2, 2
]]+1891*S[[3, 3, 1]]+4999*S[[4, 2, 1]]+5104*S[[5, 1, 1]]+294*S[[2, 2, 2, 1]]+
1456*S[[3, 2, 1, 1]]+1665*S[[4, 1, 1, 1]]+168*S[[2, 2, 1, 1, 1]]+295*S[[3, 1, 1
, 1, 1]]+27*S[[2, 1, 1, 1, 1, 1]]+S[[1, 1, 1, 1, 1, 1, 1]])+T^8*(-8*S[[1, 1, 1,
1, 1, 1, 1, 1]]-252*S[[2, 1, 1, 1, 1, 1, 1]]-1950*S[[2, 2, 1, 1, 1, 1]]-5033*S[
[2, 2, 2, 1, 1]]-3367*S[[2, 2, 2, 2]]-3332*S[[3, 1, 1, 1, 1, 1]]-22226*S[[3, 2,
1, 1, 1]]-37824*S[[3, 2, 2, 1]]-44330*S[[3, 3, 1, 1]]-44595*S[[3, 3, 2]]-23940*
S[[4, 1, 1, 1, 1]]-111758*S[[4, 2, 1, 1]]-92531*S[[4, 2, 2]]-163888*S[[4, 3, 1] ]-64140*S[[4, 4]]-100772*S[[5, 1, 1, 1]]-283126*S[[5, 2, 1]]-196272*S[[5, 3]]-\
247968*S[[6, 1, 1]]-311700*S[[6, 2]]-329328*S[[7, 1]]-181440*S[[8]]))[2]*S[[0]] )[2]*S[[0]]
SSM-Thom polynomial in Schur-tilde functions T^7 (+5040 S_{7}+8028 S_{6, 1}+6746 S_{5, 2}+3500 S_{4, 3}+5104 S_{5, 1, 1}+4999 S_{4, 2, 1}+1891 S_{3, 3, 1}+1255 S_{3, 2, 2}+1665 S_{4, 1, 1, 1}+1456 S_{3, 2, 1, 1}+294 S_{2, 2, 2, 1}+295 S_{3, 1, 1, 1, 1}+168 S_{2, 2, 1, 1, 1}+27 S_{2, 1, 1, 1, 1, 1}+1 S_{1, 1, 1, 1, 1, 1, 1})+T^8 (-141120 S_{8}-263052 S_{7, 1}-247140 S_{6, 2}-151788 S_{5, 3}-46640 S_{4, 4}-193260 S_{6, 1, 1}-222581 S_{5, 2, 1}-125828 S_{4, 3, 1}-67515 S_{4, 2, 2}-32011 S_{3, 3, 2}-72031 S_{5, 1, 1, 1}-80943 S_{4, 2, 1, 1}-30942 S_{3, 3, 1, 1}-26098 S_{3, 2, 2, 1}-1897 S_{2, 2, 2, 2}-14435 S_{4, 1, 1, 1, 1}-13557 S_{3, 2, 1, 1, 1}-2891 S_{2, 2, 2, 1, 1}-1481 S_{3, 1, 1, 1, 1, 1}-861 S_{2, 2, 1, 1, 1, 1}-61 S_{2, 1, 1, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^2+y^5)
Thom-Boardman class \Sigma^{2,0}
Codimension 7
SSM-Thom polynomial in Chern classes (-2 c_{1}^4 c_{3}+ 2 c_{1}^3 c_{2}^2-9 c_{1}^3 c_{4}+ 9 c_{1} c_{2}^3-26 c_{1}^2 c_{5}+ 29 c_{1} c_{2} c_{4}-17 c_{1} c_{3}^2+ 14 c_{2}^2 c_{3}-24 c_{1} c_{6}+ 34 c_{2} c_{5}-10 c_{3} c_{4}) T^7+ (14 c_{1}^5 c_{3}-14 c_{1}^4 c_{2}^2+ 79 c_{1}^4 c_{4}-79 c_{1}^2 c_{2}^3+ 308 c_{1}^3 c_{5}-279 c_{1}^2 c_{2} c_{4}+ 193 c_{1}^2 c_{3}^2-208 c_{1} c_{2}^2 c_{3}-14 c_{2}^4+ 532 c_{1}^2 c_{6}-586 c_{1} c_{2} c_{5}+ 258 c_{1} c_{3} c_{4}-172 c_{2}^2 c_{4}-32 c_{2} c_{3}^2+ 336 c_{1} c_{7}-420 c_{2} c_{6}+ 54 c_{3} c_{5}+ 30 c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (44 s_{4, 3}+ 84 s_{5, 2}+ 47 s_{3, 2, 2}+ 30 s_{3, 3, 1}+ 82 s_{4, 2, 1}+ 13 s_{2, 2, 2, 1}+ 24 s_{3, 2, 1, 1}+ 2 s_{2, 2, 1, 1, 1}) T^7+ (-14 s_{2, 2, 1, 1, 1, 1}-121 s_{2, 2, 2, 1, 1}-121 s_{2, 2, 2, 2}-214 s_{3, 2, 1, 1, 1}-836 s_{3, 2, 2, 1}-522 s_{3, 3, 1, 1}-855 s_{3, 3, 2}-1102 s_{4, 2, 1, 1}-1635 s_{4, 2, 2}-1804 s_{4, 3, 1}-532 s_{4, 4}-2354 s_{5, 2, 1}-1744 s_{5, 3}-1788 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^7 (+84 S_{5, 2}+44 S_{4, 3}+82 S_{4, 2, 1}+30 S_{3, 3, 1}+47 S_{3, 2, 2}+24 S_{3, 2, 1, 1}+13 S_{2, 2, 2, 1}+2 S_{2, 2, 1, 1, 1})+T^8 (-1284 S_{6, 2}-1188 S_{5, 3}-312 S_{4, 4}-1692 S_{5, 2, 1}-1224 S_{4, 3, 1}-1119 S_{4, 2, 2}-547 S_{3, 3, 2}-678 S_{4, 2, 1, 1}-306 S_{3, 3, 1, 1}-513 S_{3, 2, 2, 1}-56 S_{2, 2, 2, 2}-88 S_{3, 2, 1, 1, 1}-48 S_{2, 2, 2, 1, 1}-2 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^3+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 7
SSM-Thom polynomial in Chern classes (-2 c_{1}^4 c_{3}+ 2 c_{1}^3 c_{2}^2-7 c_{1}^3 c_{4}+ 8 c_{1}^2 c_{2} c_{3}-c_{1} c_{2}^3-6 c_{1}^2 c_{5}-5 c_{1} c_{2} c_{4}+ 13 c_{1} c_{3}^2-2 c_{2}^2 c_{3}-10 c_{2} c_{5}+ 10 c_{3} c_{4}) T^7+ (14 c_{1}^5 c_{3}-14 c_{1}^4 c_{2}^2+ 63 c_{1}^4 c_{4}-64 c_{1}^3 c_{2} c_{3}+ c_{1}^2 c_{2}^3+ 97 c_{1}^3 c_{5}+ 25 c_{1}^2 c_{2} c_{4}-128 c_{1}^2 c_{3}^2+ 3 c_{1} c_{2}^2 c_{3}+ 3 c_{2}^4+ 54 c_{1}^2 c_{6}+ 126 c_{1} c_{2} c_{5}-194 c_{1} c_{3} c_{4}+ 30 c_{2}^2 c_{4}-16 c_{2} c_{3}^2+ 94 c_{2} c_{6}-63 c_{3} c_{5}-31 c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (44 s_{4, 3}+ 12 s_{5, 2}+ 9 s_{3, 2, 2}+ 30 s_{3, 3, 1}+ 22 s_{4, 2, 1}+ 3 s_{2, 2, 2, 1}+ 12 s_{3, 2, 1, 1}+ 2 s_{2, 2, 1, 1, 1}) T^7+ (-14 s_{2, 2, 1, 1, 1, 1}-41 s_{2, 2, 2, 1, 1}-24 s_{2, 2, 2, 2}-118 s_{3, 2, 1, 1, 1}-222 s_{3, 2, 2, 1}-390 s_{3, 3, 1, 1}-399 s_{3, 3, 2}-358 s_{4, 2, 1, 1}-331 s_{4, 2, 2}-1108 s_{4, 3, 1}-580 s_{4, 4}-458 s_{5, 2, 1}-880 s_{5, 3}-204 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^7 (+12 S_{5, 2}+44 S_{4, 3}+22 S_{4, 2, 1}+30 S_{3, 3, 1}+9 S_{3, 2, 2}+12 S_{3, 2, 1, 1}+3 S_{2, 2, 2, 1}+2 S_{2, 2, 1, 1, 1})+T^8 (-132 S_{6, 2}-612 S_{5, 3}-360 S_{4, 4}-312 S_{5, 2, 1}-768 S_{4, 3, 1}-207 S_{4, 2, 2}-243 S_{3, 3, 2}-222 S_{4, 2, 1, 1}-222 S_{3, 3, 1, 1}-129 S_{3, 2, 2, 1}-9 S_{2, 2, 2, 2}-52 S_{3, 2, 1, 1, 1}-18 S_{2, 2, 2, 1, 1}-2 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(x^2,y^3)
Thom-Boardman class \Sigma^{2,1,0}
Codimension 7
SSM-Thom polynomial in Chern classes (-2 c_{1}^2 c_{2} c_{3}+ 2 c_{1} c_{2}^3-4 c_{1} c_{2} c_{4}+ 2 c_{1} c_{3}^2+ 2 c_{2}^2 c_{3}-2 c_{2} c_{5}+ 2 c_{3} c_{4}) T^7+ (10 c_{1}^3 c_{2} c_{3}-10 c_{1}^2 c_{2}^3+ 27 c_{1}^2 c_{2} c_{4}-10 c_{1}^2 c_{3}^2-14 c_{1} c_{2}^2 c_{3}-3 c_{2}^4+ 27 c_{1} c_{2} c_{5}-17 c_{1} c_{3} c_{4}-6 c_{2}^2 c_{4}-4 c_{2} c_{3}^2+ 10 c_{2} c_{6}-9 c_{3} c_{5}-c_{4}^2) T^8
SSM-Thom polynomial in Schur functions (8 s_{4, 3}+ 4 s_{5, 2}+ 6 s_{3, 2, 2}+ 6s_{3, 3, 1}+ 6s_{4, 2, 1}+ 2s_{2, 2, 2, 1}+ 2s_{3, 2, 1, 1}) T^7+ (-10 s_{2, 2, 2, 1, 1}-13 s_{2, 2, 2, 2}-10 s_{3, 2, 1, 1, 1}-63 s_{3, 2, 2, 1}-50 s_{3, 3, 1, 1}-81 s_{3, 3, 2}-50 s_{4, 2, 1, 1}-93 s_{4, 2, 2}-148 s_{4, 3, 1}-68 s_{4, 4}-80 s_{5, 2, 1}-108 s_{5, 3}-40 s_{6, 2}) T^8
SSM-Thom polynomial in Schur-tilde functions T^7 (+4 S_{5, 2}+8 S_{4, 3}+6 S_{4, 2, 1}+6 S_{3, 3, 1}+6 S_{3, 2, 2}+2 S_{3, 2, 1, 1}+2 S_{2, 2, 2, 1})+T^8 (-16 S_{6, 2}-52 S_{5, 3}-28 S_{4, 4}-38 S_{5, 2, 1}-76 S_{4, 3, 1}-45 S_{4, 2, 2}-33 S_{3, 3, 2}-18 S_{4, 2, 1, 1}-18 S_{3, 3, 1, 1}-25 S_{3, 2, 2, 1}-3 S_{2, 2, 2, 2})

codimension 8

Local algebra C[x]/(x^9)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,1,1,0}
Codimension 8
SSM-Thom polynomial in Chern classes (c_{1}^8+ 28 c_{1}^6 c_{2}+ 140 c_{1}^4 c_{2}^2+ 140 c_{1}^2 c_{2}^3+ 14 c_{2}^4+ 182 c_{1}^5 c_{3}+ 868 c_{1}^3 c_{2} c_{3}+ 501 c_{1} c_{2}^2 c_{3}+ 642 c_{1}^2 c_{3}^2+ 202 c_{2} c_{3}^2+ 952 c_{1}^4 c_{4}+ 2229 c_{1}^2 c_{2} c_{4}+ 364 c_{2}^2 c_{4}+ 1559 c_{1} c_{3} c_{4}+ 332 c_{4}^2+ 3383 c_{1}^3 c_{5}+ 3455 c_{1} c_{2} c_{5}+ 954 c_{3} c_{5}+ 7552 c_{1}^2 c_{6}+ 2314 c_{2} c_{6}+ 9468 c_{1} c_{7}+ 5040 c_{8})T^8
SSM-Thom polynomial in Schur functions (s_{1, 1, 1, 1, 1, 1, 1, 1}+ 35 s_{2, 1, 1, 1, 1, 1, 1}+ 300 s_{2, 2, 1, 1, 1, 1}+ 840 s_{2, 2, 2, 1, 1}+ 588 s_{2, 2, 2, 2}+ 511 s_{3, 1, 1, 1, 1, 1}+ 3732 s_{3, 2, 1, 1, 1}+ 6759 s_{3, 2, 2, 1}+ 8031 s_{3, 3, 1, 1}+ 8412 s_{3, 3, 2}+ 4025 s_{4, 1, 1, 1, 1}+ 20259 s_{4, 2, 1, 1}+ 17484 s_{4, 2, 2}+ 31584 s_{4, 3, 1}+ 12964 s_{4, 4}+ 18424 s_{5, 1, 1, 1}+ 54822 s_{5, 2, 1}+ 39764 s_{5, 3}+ 48860 s_{6, 1, 1}+ 63808 s_{6, 2}+ 69264 s_{7, 1}+ 40320 s_{8})T^8
SSM-Thom polynomial in Schur-tilde functions T^8 (+40320 S_{8}+69264 S_{7, 1}+63808 S_{6, 2}+39764 S_{5, 3}+12964 S_{4, 4}+48860 S_{6, 1, 1}+54822 S_{5, 2, 1}+31584 S_{4, 3, 1}+17484 S_{4, 2, 2}+8412 S_{3, 3, 2}+18424 S_{5, 1, 1, 1}+20259 S_{4, 2, 1, 1}+8031 S_{3, 3, 1, 1}+6759 S_{3, 2, 2, 1}+588 S_{2, 2, 2, 2}+4025 S_{4, 1, 1, 1, 1}+3732 S_{3, 2, 1, 1, 1}+840 S_{2, 2, 2, 1, 1}+511 S_{3, 1, 1, 1, 1, 1}+300 S_{2, 2, 1, 1, 1, 1}+35 S_{2, 1, 1, 1, 1, 1, 1}+1 S_{1, 1, 1, 1, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^2+y^6)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes (-120 c_{1} c_{7}+ 7 c_{2}^4-3 c_{4}^2+ 2 c_{1}^4 c_{2}^2-2 c_{1}^5 c_{3}-53 c_{1}^2 c_{3}^2+ 4 c_{2} c_{3}^2-14 c_{1}^4 c_{4}+ 74 c_{2}^2 c_{4}-71 c_{1}^3 c_{5}-39 c_{3} c_{5}-154 c_{1}^2 c_{6}+ 162 c_{2} c_{6}+ 60 c_{1}^2 c_{2} c_{4}-90 c_{1} c_{3} c_{4}+ 166 c_{1} c_{2} c_{5}+ 18 c_{1}^2 c_{2}^3-4 c_{1}^3 c_{2} c_{3}+ 57 c_{1} c_{2}^2 c_{3})T^8
SSM-Thom polynomial in Schur functions (2 s_{2, 2, 1, 1, 1, 1}+ 24 s_{2, 2, 2, 1, 1}+ 29 s_{2, 2, 2, 2}+ 40 s_{3, 2, 1, 1, 1}+ 194 s_{3, 2, 2, 1}+ 108 s_{3, 3, 1, 1}+ 194 s_{3, 3, 2}+ 250 s_{4, 2, 1, 1}+ 424 s_{4, 2, 2}+ 406 s_{4, 3, 1}+ 124 s_{4, 4}+ 620 s_{5, 2, 1}+ 412 s_{5, 3}+ 528 s_{6, 2})T^8
SSM-Thom polynomial in Schur-tilde functions T^8 (+528 S_{6, 2}+412 S_{5, 3}+124 S_{4, 4}+620 S_{5, 2, 1}+406 S_{4, 3, 1}+424 S_{4, 2, 2}+194 S_{3, 3, 2}+250 S_{4, 2, 1, 1}+108 S_{3, 3, 1, 1}+194 S_{3, 2, 2, 1}+29 S_{2, 2, 2, 2}+40 S_{3, 2, 1, 1, 1}+24 S_{2, 2, 2, 1, 1}+2 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^3+y^5)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes (-4 c_{2}^4-20 c_{4}^2+ 2 c_{1}^4 c_{2}^2-2 c_{1}^5 c_{3}+ 13 c_{1}^2 c_{3}^2+ 24 c_{2} c_{3}^2-11 c_{1}^4 c_{4}-32 c_{2}^2 c_{4}-26 c_{1}^3 c_{5}+ 60 c_{3} c_{5}-24 c_{1}^2 c_{6}-40 c_{2} c_{6}+ 7 c_{1}^2 c_{2} c_{4}+ 34 c_{1} c_{3} c_{4}-2 c_{1} c_{2} c_{5}+ 3 c_{1}^2 c_{2}^3+ 8 c_{1}^3 c_{2} c_{3}+ 10 c_{1} c_{2}^2 c_{3})T^8
SSM-Thom polynomial in Schur functions (2 s_{2, 2, 1, 1, 1, 1}+ 9 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 22 s_{3, 2, 1, 1, 1}+ 48 s_{3, 2, 2, 1}+ 66 s_{3, 3, 1, 1}+ 99 s_{3, 3, 2}+ 82 s_{4, 2, 1, 1}+ 75 s_{4, 2, 2}+ 232 s_{4, 3, 1}+ 76 s_{4, 4}+ 122 s_{5, 2, 1}+ 232 s_{5, 3}+ 60 s_{6, 2})T^8
SSM-Thom polynomial in Schur-tilde functions T^8 (+60 S_{6, 2}+232 S_{5, 3}+76 S_{4, 4}+122 S_{5, 2, 1}+232 S_{4, 3, 1}+75 S_{4, 2, 2}+99 S_{3, 3, 2}+82 S_{4, 2, 1, 1}+66 S_{3, 3, 1, 1}+48 S_{3, 2, 2, 1}+3 S_{2, 2, 2, 2}+22 S_{3, 2, 1, 1, 1}+9 S_{2, 2, 2, 1, 1}+2 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(xy,x^4+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes (-5 c_{1}^4 c_{4}+ 23 c_{4}^2+ 2 c_{2}^4+ 13 c_{2}^2 c_{4}+ c_{1}^4 c_{2}^2- c_{1}^5 c_{3}-11 c_{2} c_{3}^2-6 c_{1}^3 c_{5}-21 c_{3} c_{5}-2 c_{2} c_{6}+ 18 c_{1}^2 c_{3}^2-29 c_{1} c_{2} c_{5}- c_{1}^2 c_{2}^3-9 c_{1}^2 c_{2} c_{4}+ 27 c_{1} c_{3} c_{4}-5 c_{1} c_{2}^2 c_{3}+ 6 c_{1}^3 c_{2} c_{3})T^8
SSM-Thom polynomial in Schur functions (s_{2, 2, 1, 1, 1, 1}+ 2 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 8 s_{3, 2, 1, 1, 1}+ 15 s_{3, 2, 2, 1}+ 36 s_{3, 3, 1, 1}+ 21 s_{3, 3, 2}+ 23 s_{4, 2, 1, 1}+ 25 s_{4, 2, 2}+ 95 s_{4, 3, 1}+ 86 s_{4, 4}+ 28 s_{5, 2, 1}+ 62 s_{5, 3}+ 12 s_{6, 2})T^8
SSM-Thom polynomial in Schur-tilde functions T^8 (+12 S_{6, 2}+62 S_{5, 3}+86 S_{4, 4}+28 S_{5, 2, 1}+95 S_{4, 3, 1}+25 S_{4, 2, 2}+21 S_{3, 3, 2}+23 S_{4, 2, 1, 1}+36 S_{3, 3, 1, 1}+15 S_{3, 2, 2, 1}+3 S_{2, 2, 2, 2}+8 S_{3, 2, 1, 1, 1}+2 S_{2, 2, 2, 1, 1}+1 S_{2, 2, 1, 1, 1, 1})
Local algebra C[x,y]/(x^2+y^3,xy^2)
Thom-Boardman class \Sigma^{2,1}
Codimension 8
SSM-Thom polynomial in Chern classes (2 c_{1}^2 c_{2}^3+ c_{2}^4-2 c_{1}^3 c_{2} c_{3}+ 4 c_{1} c_{2}^2 c_{3}+ 2 c_{1}^2 c_{3}^2+ 2 c_{2} c_{3}^2-7 c_{1}^2 c_{2} c_{4}+ 2 c_{2}^2 c_{4}+ 5 c_{1} c_{3} c_{4}+ c_{4}^2-9 c_{1} c_{2} c_{5}+ 3 c_{3} c_{5}-4 c_{2} c_{6})T^8
SSM-Thom polynomial in Schur functions (2 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 2 s_{3, 2, 1, 1, 1}+ 15 s_{3, 2, 2, 1}+ 12 s_{3, 3, 1, 1}+ 21 s_{3, 3, 2}+ 12 s_{4, 2, 1, 1}+ 25 s_{4, 2, 2}+ 40 s_{4, 3, 1}+ 20 s_{4, 4}+ 22 s_{5, 2, 1}+ 32 s_{5, 3}+ 12 s_{6, 2})T^8
SSM-Thom polynomial in Schur-tilde functions T^8 (+12 S_{6, 2}+32 S_{5, 3}+20 S_{4, 4}+22 S_{5, 2, 1}+40 S_{4, 3, 1}+25 S_{4, 2, 2}+21 S_{3, 3, 2}+12 S_{4, 2, 1, 1}+12 S_{3, 3, 1, 1}+15 S_{3, 2, 2, 1}+3 S_{2, 2, 2, 2}+2 S_{3, 2, 1, 1, 1}+2 S_{2, 2, 2, 1, 1})